1.1 --- a/src/HOL/Power.thy Fri Mar 05 15:26:04 2004 +0100
1.2 +++ b/src/HOL/Power.thy Fri Mar 05 15:26:14 2004 +0100
1.3 @@ -171,13 +171,13 @@
1.4 by (simp add: divide_inverse power_mult_distrib nonzero_power_inverse)
1.5
1.6 lemma power_divide:
1.7 - "(a/b) ^ n = ((a::'a::{field,division_by_zero,ringpower}) ^ n/ b ^ n)"
1.8 + "(a/b) ^ n = ((a::'a::{field,division_by_zero,ringpower}) ^ n / b ^ n)"
1.9 apply (case_tac "b=0", simp add: power_0_left)
1.10 apply (rule nonzero_power_divide)
1.11 apply assumption
1.12 done
1.13
1.14 -lemma power_abs: "abs(a ^ n) = abs(a::'a::{ordered_field,ringpower}) ^ n"
1.15 +lemma power_abs: "abs(a ^ n) = abs(a::'a::{ordered_ring,ringpower}) ^ n"
1.16 apply (induct_tac "n")
1.17 apply (auto simp add: power_Suc abs_mult)
1.18 done
1.19 @@ -301,8 +301,7 @@
1.20
1.21 instance nat :: ringpower
1.22 proof
1.23 - fix z :: nat
1.24 - fix n :: nat
1.25 + fix z n :: nat
1.26 show "z^0 = 1" by simp
1.27 show "z^(Suc n) = z * (z^n)" by simp
1.28 qed